具多內部源二維多物種溶質傳輸解析解模式發展及現地應用

Abstract

在現地污染整治上常見場址內有多處污染源長期釋出的情況，然而前人發展之移流－延散方程式多為邊界源(boundary source)溶質傳輸解析解，在模擬現地場址污染問題時容易受到限制且較難廣泛應用。而考慮內部源(inner source)之溶質傳輸解析解模式可模擬流場任意位置污染源注入情形。且過去發展之單物種傳輸模式，無法模擬序列降解下多物種的衰減與傳輸情形。本研究發展具多內部源二維多物種溶質傳輸解析解模式，並考慮移流、延散、線性平衡吸附和一階衰減情況，以描述溶質在二維孔隙介質中的傳輸行為，模式亦可應用在模擬放射性核種衰變鏈、氨氮及含氯有機物之降解過程。解析解推導依續使用Laplace轉換、finite Fourier cosine轉換及廣義型積分轉換消去時間及空間微分項，將偏微分方程式轉換為代數方程式進行求解，再利用一系列逆轉換求得原域之解析解。本研究發展之解析解與有限差分(Finite difference method)數值方法進行驗證，結果顯示兩者相當吻合，確定發展模式之正確性。模式應用在Dover空軍基地第六區，模擬含氯有機溶劑污染場址PCE及TCE污染團分別在在10年、20年、30年及40年情境之分布與擴散情形，並與現地場址數據做比較，闡述模式的適用性。本研究可了解含氯有機物序列降解上多物種污染物傳輸行為，且作為現地場址初步評估污染整治的基礎。

The long term releases of multiple sources are common situation in remediation of contaminated site. However, most of the advective-dispersive equation from literatures are analytical model for solute transport developed only for boundary source, which could be limited to simulate the transport of contaminant for filed-scale site. Considering the analytical model for solute transport of inner source could simulate any position for the contaminant sources injection. The analytical model for single-species solute transport could not simulate the decay and transport of multispecies in the condition of sequential decay chain. This study presents an multiple sources analytical model for two-dimensional multi-species advective-dispersive equation which considered linear equilibrium sorption and first order decay reaction. The model could also be applied in predicting the behavior of decaying contaminant such as radionuclide, nitrogen transformation and dissolved chlorinated solvent. Generalized analytical solutions are derived through the sequential application of the Laplace, finite Fourier cosine and generalized integral transform to remove the temporal and spatial derivatives in the coupled partial differential equation. The system of coupled partial differential equation is tranform to a set of linear algebraic equations, and the solutions in the original domain are then obtained through consecutive integral transform inversions. The developed analytical solution is tested by comparing their results against the numerical solutions using a finite difference scheme. Results show perfect agreements between the analytical and numerical solutions. The developed model was applied to analyze field-scale transport and biodegradation processes occurring at the Area-6 site in Dover Air Force Base, and predict the distribution of PCE and TCE plumes in different scenario (10 years, 20 years, 30 years and 40 years). The developed model in this study is a useful tool for simulation sequential decay reactions between multispecies, and a foundation of a preliminary assessment to the remediation of the field site.